The saddlepoint method and portfolio optionalities

This short communication describes the application of saddlepoint methods in the calculation of tranche payouts and expected shortfall (ESF, also known as conditional value-at-risk) from the distribution of portfolio losses. These are closely related quantities that are fundamental to the valuation of collateralised debt obligation tranches (Andersen, Sidenius & Basu, 2003) and credit portfolio management (Martin, 2004). Whereas the density and tail probability are well understood, the latter re